Solve 5y^2-(y-2)(3y+1)-2(y+1)(y-5)

$$5 y ^ { 2 } - ( y - 2 ) ( 3 y + 1 ) - 2 ( y + 1 ) ( y - 5 )$$

Evaluate

$$13y+12$$

Solution Steps

Use the distributive property to multiply y-2 by 3y+1 and combine like terms.

$$5y^{2}-\left(3y^{2}-5y-2\right)-2\left(y+1\right)\left(y-5\right)$$

To find the opposite of 3y^{2}-5y-2, find the opposite of each term.

$$5y^{2}-3y^{2}+5y+2-2\left(y+1\right)\left(y-5\right)$$

Combine 5y^{2} and -3y^{2} to get 2y^{2}.

$$2y^{2}+5y+2-2\left(y+1\right)\left(y-5\right)$$

Use the distributive property to multiply -2 by y+1.

$$2y^{2}+5y+2+\left(-2y-2\right)\left(y-5\right)$$

Use the distributive property to multiply -2y-2 by y-5 and combine like terms.

$$2y^{2}+5y+2-2y^{2}+8y+10$$

Combine 2y^{2} and -2y^{2} to get 0.

$$5y+2+8y+10$$

Combine 5y and 8y to get 13y.

$$13y+2+10$$

Add 2 and 10 to get 12.

$$13y+12$$

Expand

$$13y+12$$

Solution Steps

Use the distributive property to multiply y-2 by 3y+1 and combine like terms.

$$5y^{2}-\left(3y^{2}-5y-2\right)-2\left(y+1\right)\left(y-5\right)$$

To find the opposite of 3y^{2}-5y-2, find the opposite of each term.

$$5y^{2}-3y^{2}+5y+2-2\left(y+1\right)\left(y-5\right)$$

Combine 5y^{2} and -3y^{2} to get 2y^{2}.

$$2y^{2}+5y+2-2\left(y+1\right)\left(y-5\right)$$

Use the distributive property to multiply -2 by y+1.

$$2y^{2}+5y+2+\left(-2y-2\right)\left(y-5\right)$$

Use the distributive property to multiply -2y-2 by y-5 and combine like terms.

$$2y^{2}+5y+2-2y^{2}+8y+10$$

Combine 2y^{2} and -2y^{2} to get 0.

$$5y+2+8y+10$$

Combine 5y and 8y to get 13y.

$$13y+2+10$$

Add 2 and 10 to get 12.

$$13y+12$$